U.S. patent number 10,983,007 [Application Number 16/521,603] was granted by the patent office on 2021-04-20 for material optical transition analysis method and system.
This patent grant is currently assigned to HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY. The grantee listed for this patent is HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY. Invention is credited to Xiuguo Chen, Mingsheng Fang, Honggang Gu, Hao Jiang, Shiyuan Liu, Baokun Song.
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United States Patent |
10,983,007 |
Gu , et al. |
April 20, 2021 |
Material optical transition analysis method and system
Abstract
A material optical transition analysis method and system are
provided, the method includes: determining a dielectric function
spectrum of a material to be analyzed, calculating a second
derivative spectrum of the dielectric function spectrum related to
the excitation light energy, and performing the CP fitting analysis
on the second derivative spectrum to obtain a CP analysis result
diagram of the material; drawing an energy band structure diagram
and a PDOS diagram of the material, and drawing an energy
difference diagram between CBs and VBs according to the energy band
structure diagram of the material; determining spatial positions of
CPs and the corresponding CBs and the VBs according to the CP
analysis result diagram of the material and the energy difference
diagram between the CBs and the VBs; and finally indicating the CBs
and the VBs in the energy band structure diagram, and determining
the particle types participating in formation of the CPs in the
PDOS diagram to complete the material optical transition analysis.
The invention realizes the analysis and interpretation of the
optical transition characteristics occurring at the materials from
the perspective of physics, which has the advantages of reliable
operation process system and accurate and reliable analysis
results.
Inventors: |
Gu; Honggang (Hubei,
CN), Song; Baokun (Hubei, CN), Liu;
Shiyuan (Hubei, CN), Fang; Mingsheng (Hubei,
CN), Chen; Xiuguo (Hubei, CN), Jiang;
Hao (Hubei, CN) |
Applicant: |
Name |
City |
State |
Country |
Type |
HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY |
Hubei |
N/A |
CN |
|
|
Assignee: |
HUAZHONG UNIVERSITY OF SCIENCE AND
TECHNOLOGY (Hubei, CN)
|
Family
ID: |
1000005499921 |
Appl.
No.: |
16/521,603 |
Filed: |
July 25, 2019 |
Prior Publication Data
|
|
|
|
Document
Identifier |
Publication Date |
|
US 20200333188 A1 |
Oct 22, 2020 |
|
Foreign Application Priority Data
|
|
|
|
|
Apr 16, 2019 [CN] |
|
|
201910301515.8 |
|
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G01J
3/443 (20130101); G01N 21/63 (20130101) |
Current International
Class: |
G01J
3/443 (20060101); G01N 21/63 (20060101) |
Field of
Search: |
;356/300 |
References Cited
[Referenced By]
U.S. Patent Documents
Other References
Wei Li, "Broadband optical properties of large-area monolayer CVD
molybdenum disulfide", Physical Review B, Nov. 21, 2014, pp. 1-8.
cited by applicant .
Aurelien M. A. Leguy, "Experimental and theoretical optical
properties of methylammonium lead halide perovskites", Nanoscale,
Aug. 2016, pp. 6317-6327. cited by applicant .
Masaki Shirayama, "Optical transitions in hybrid perovskite solar
cells: Ellipsometry, density functional theory, and quantum
efficiency analyses for CH3NH3Pbl3", Physical Review Applied, Jan.
27, 2016, pp. 1-25. cited by applicant.
|
Primary Examiner: Chowdhury; Tarifur R
Assistant Examiner: Nixon; Omar H
Attorney, Agent or Firm: JCIPRNET
Claims
What is claimed is:
1. A material optical transition analysis method, comprising: S1:
determining a dielectric function spectrum of a material to be
analyzed, calculating a second derivative spectrum of the
dielectric function spectrum with respect to excitation light
energy, and performing critical point (CP) fitting analysis on the
second derivative spectrum to obtain a CP analysis result diagram
of the material; S2: drawing an energy band structure diagram and a
Partial Density of States (PDOS) diagram of the material, and
drawing an energy difference diagram between conduction bands (CBs)
and valence bands (VBs) according to the energy band structure
diagram of the material; S3: determining spatial positions of CPs
and the corresponding CBs and the VBs according to the CP analysis
result diagram of the material and the energy difference diagram
between the CBs and the VBs; and S4: indicating the CBs and the VBs
in the energy band structure diagram, and determining the particle
types participating in formation of the CPs in the PDOS diagram
according to the energy band structure diagram with the indicated
CBs and VBs, so as to complete the material optical transition
analysis, wherein the step S4 of determining the type of the
particles participating in formation of the CPs comprises: drawing
the PDOS diagram at one side of the energy band structure diagram,
so that the energy ranges of the longitudinal coordinates thereof
and the longitudinal coordinates of the band structure diagram are
consistent, and the scales of the two longitudinal coordinates are
aligned; and drawing straight lines horizontally from the CBs and
the VBs indicated in the energy band structure diagram and
extending the same to the PDOS diagram, and directly reading out
the type of the particles participating in the formation of the CPs
in the PDOS diagram by analyzing intersections of the straight
lines with spectral lines in the PDOS diagram.
2. The material optical transition analysis method as claimed in
claim 1, wherein the step S3 of determining the spatial positions
of the CPs and the corresponding CBs and the VBs comprises:
horizontally drawing the obtained material CP analysis result
diagram and the energy difference diagram between the CBs and the
VBs side by side, such that energy ranges and scales of
longitudinal coordinates of the two diagrams are completely
consistent and aligned; using a series of horizontal lines to
indicate positions of the CPs in the CP analysis result diagram,
making the horizontal lines to horizontally traverse into the
energy difference diagram, and determining the CBs and the VBs
participating in the formation of the CPs according to tangent
points of the horizontal lines and curves in the energy difference
diagram; and determining the spatial positions of the CPs by
indicating the above-mentioned tangent points in the Brillouin zone
(BZ).
3. The material optical transition analysis method as claimed in
claim 2, wherein the step S4 of indicating the CBs and the VBs in
the energy band structure diagram comprises: drawing the energy
band structure diagram of the step S2 right above the energy
difference diagram to make it consistent with the BZ high symmetry
points covered by horizontal coordinates of the energy difference
diagram, wherein scales of the high symmetry points in the two
diagrams are aligned with each other; and drawing a straight line
perpendicular to the upper energy band structure diagram from the
tangent points on the curves of the energy difference diagram,
wherein two points where the straight line intersects with the
energy band structure diagram indicate the CBs and the VBs
participating in formation of the CPs, so as to indicate the CBs
and the VBs in the energy band structure diagram.
Description
CROSS-REFERENCE TO RELATED APPLICATION
This application claims the priority benefits of China application
serial no. 201910301515.8, filed on Apr. 16, 2019. The entirety of
the above-mentioned patent application is hereby incorporated by
reference herein and made a part of specification.
BACKGROUND
Technical Field
The invention relates to a material measurement and
characterization research field, and particularly relates to a
material optical transition analysis method and system, which are
adapted to analysis and research of optical transitions of various
materials.
Description of Related Art
Along with advent of an information age in the 21.sup.st century,
optical properties of materials have attracted great attention.
Especially the discovery of graphene in 2004 triggered extensive
research on low-dimensional material science by researchers, after
which a large number of miniaturized and quantized optical devices
were designed and manufactured. However, performance of these
optical devices largely depends on intrinsic optical properties of
the related materials, especially microscopic optical transition
properties of the materials. Therefore, accurate analysis and
research of material optical transitions are very important for the
design and optimization of the corresponding optical devices.
Main parameters for quantitatively describing a material optical
property include: the dielectric function, the complex refractive
index and the complex optical conductivity, and these three
parameters can be deduced from each other under certain conditions.
It can be said that these three basic optical parameters can
directly influence the working performance of corresponding optical
devices (such as: photodetectors, field effect transistors, solar
cells, sensors, etc.). Presently, measurement and characterization
of these basic optical parameters mainly include three methods of
reflection (absorption) spectroscopy, contrast spectroscopy and
ellipsometry. Although the methods used to determine the basic
optical parameters are relatively mature, the in-depth analysis of
optical transition characteristics implied in the basic optical
parameters is still insufficient after the basic optical parameters
are obtained. There is no systematic method or process for
analyzing the material optical transition characteristics at
present, which also limits an in-depth optimization design of the
corresponding optical devices.
With the aid of first-principles calculations based on the density
functional theory, scientists can substantially predict the
dispersion rule of the dielectric function or the complex
refractive index of materials, and qualitatively explain the
underlying physical mechanisms of the optical transitions. In
recent years, along with the disclosure and development of some
hybrid functionals, the reliability of the material basic optical
parameter spectrum obtained through theoretical calculation is
further improved, but there are still problems such as insufficient
strength and feature mismatch, etc., which makes theoretical
analysis of the material optical transition still having greater
uncertainty, this is mainly because that the proposed hybrid
functionals cannot accurately describe internal
exchange-correlation potential in the materials. At present, the
widely accepted GW-BSE (Bethe-Salpeter Equation) theory which can
accurately predict the material basic optical parameter spectrum
requires very expensive computational resources to obtain
relatively reliable optical parameter spectrum. For the materials
with a large number of atoms in primitive cells, the optical
parameter prediction based on the GW-BSE theory is also becoming
impractical at present. Therefore, in most cases, it is unrealistic
to analyze the optical transition mechanisms of the materials by
directly comparing the material optical parameter spectrum measured
through experiment with the theoretically calculated optical
parameter spectrum. In order to avoid such difficulty, scientists
have found that the calculated energy band structure and the
Partial Density of States (PDOS) of the material can reflect the
optical transition information of the material to some extent.
Compared with the direct calculation of the optical parameter
spectrum of the material, the calculation of the energy band
structure and the PDOS is much easier and has high accuracy. At
present, some research groups measure optical parameter spectrum of
materials from the perspectives of theory and experiment and
analyze the optical transitions of the materials, for example, Li
et al., of Peking university (Broadband optical properties of
large-area monolayer CVD molybdenum disulfide, Physical Review B,
2014, 90: 195434) measured dielectric function spectrum of
monolayer molybdenum disulfide (MoS.sub.2) by means of a
spectroscopic ellipsometer, and combined with a critical point (CP)
analysis theory, they determined and explained some CPs on the
dielectric function spectrum, and theoretically speculated the
corresponding optical transition mechanism of these CPs. However, a
reliable theoretical basis and a detailed analysis flow of the
inference are not given, and the energy band structure and the PDOS
are not introduced to further describe the optical transition
details of the CPs in the dielectric function spectrum. Leguy et
al. (Experimental and theoretical optical properties of
methylammonium lead halide perovskites, Nanoscale, 2016, 8:
6317-6327) used ellipsometry to obtain a dielectric function
spectrum of lead-based perovskite, and obtained the energy band
structure of the lead-based perovskite through first-principles
calculations, and finally determined optical transition types
corresponding to some CPs in the dielectric function spectrum of
the lead-based perovskite by introducing an energy band nesting
theory. Such method is more systematic, but a more reliable method
for the center energy identification of the CPs is not provided.
Shirayama et al. (Optical Transitions in Hybrid Perovskite Solar
Cells: Ellipsometry, Density Functional Theory and Quantum
Efficiency Analyses for CH.sub.3NH.sub.3PbI.sub.3, Physical Review
Applied, 2016, 5: 014012) studied transition properties of
organic-inorganic hybrid perovskites by means of first-principles
calculations and ellipsometry, and introduced a CP analysis theory.
However, these theories are not organically combined with the
experimental results, and the explanation for the optical
transitions corresponding to the CPs is mainly based on the
theoretical calculation results.
SUMMARY
In view of the above shortcomings or improvement requirements of
the prior art, the invention provides a material optical transition
analysis method and system, which use a material dielectric
function spectrum, a CP theory, an energy band structure diagram, a
PDOS diagram and an energy difference diagram of conduction bands
(CBs) and valence bands (VBs) to perform analysis and
interpretation on material optical transition in a physical level,
so as to obtain a specific position of the optical transition, a
relevant energy level and a related particle type, etc., and
realize analysis and interpretation of the optical transition
characteristics of the material in the physical level, which has
the advantages of reliable operation process system and accurate
and reliable analysis results.
In order to achieve the above purpose, according to one aspect of
the invention, a material optical transition analysis method is
proposed, which includes the following steps:
S1: determining a dielectric function spectrum of a material to be
analyzed, calculating a second derivative spectrum of the
dielectric function spectrum with respect to excitation light
energy, and performing a CP fitting analysis on the second
derivative spectrum to obtain a CP analysis result diagram of the
material;
S2: drawing an energy band structure diagram and a PDOS diagram of
the material, and drawing an energy difference diagram between CBs
and VBs according to the energy band structure diagram of the
material;
S3: determining spatial positions of CPs and the corresponding CBs
and the VBs according to the CP analysis result diagram of the
material and the energy difference diagram between the CBs and the
VBs; and
S4: indicating the CBs and the VBs in the energy band structure
diagram, and determining the particle types participating in
formation of the CPs in the PDOS diagram according to the energy
band structure diagram with the indicated CBs and VBs, so as to
complete the material optical transition analysis.
Preferably, the step S3 of determining the spatial positions of the
CPs and the corresponding CBs and the VBs includes following
steps:
horizontally drawing the obtained material CP analysis result
diagram and the energy difference diagram between the CBs and the
VBs side by side, such that energy ranges and scales of
longitudinal coordinates of the two diagrams are completely
consistent and aligned;
using a series of horizontal lines to indicate positions of the CPs
in the CP analysis result diagram, making the horizontal lines to
traverse into the energy difference diagram, and determining the
CBs and the VBs participating in the formation of the CPs according
to tangent points of the horizontal lines and the energy difference
curves; and
determining the spatial positions of the CPs by indicating the
above-mentioned tangent points in the Brillouin zone (BZ).
Preferably, the step S4 of indicating the CBs and the VBs in the
energy band structure diagram includes:
drawing the energy band structure diagram of the step S2 right
above the energy difference diagram to make it consistent with the
high symmetry points of the BZ covered by horizontal coordinates of
the energy difference diagram, where scales of the high symmetry
points in the two diagrams are aligned with each other; and
drawing a straight line perpendicular to the upper energy band
structure diagram from the tangent points on the curves of the
energy difference diagram, wherein two points where the straight
line intersects with the energy band structure diagram indicate the
CBs and the VBs participating in formation of the CPs, so as to
indicate the CBs and the VBs in the energy band structure
diagram.
Preferably, the step S4 of determining the type of the particles
participating in formation of the CPs includes:
drawing the PDOS diagram at one side of the energy band structure
diagram, so that the energy ranges of the longitudinal coordinates
thereof and the longitudinal coordinates of the band structure
diagram are consistent, and the scales of the two longitudinal
coordinates are aligned; and
drawing straight lines horizontally from the CBs and the VBs
indicated in the energy band structure diagram and extending the
same to the PDOS diagram, and directly reading out the type of the
particles participating in the formation of the CPs in the PDOS
diagram by analyzing intersections of the straight lines with
spectral lines in the PDOS diagram.
According to another aspect, the invention provides a material
optical transition analysis system including:
a CP analysis module, configured to determine a dielectric function
spectrum of a material to be analyzed, and calculate a second
derivative spectrum of the dielectric function spectrum with
respect to excitation light energy, and perform CP analysis on the
second derivative spectrum to obtain a CP analysis result diagram
of the material;
an energy difference calculation module, configured to draw an
energy band structure diagram and a PDOS diagram of the material,
and draw an energy difference diagram between CBs and VBs according
to the energy band structure diagram of the material;
an energy level and position determination module, configured to
determine spatial positions of CPs and the corresponding CBs and
the VBs according to the CP analysis result diagram of the material
and the energy difference diagram between the CBs and the VBs;
and
a particle type determination module, configured to indicate the
CBs and the VBs in the energy band structure diagram, and determine
particle types participating in the formation of the CPs in the
PDOS diagram according to the energy band structure diagram with
the indicated CBs and VBs, so as to complete the material optical
transition analysis.
Preferably, the energy level and position determination module
adopts following steps to determine the spatial positions of the
CPs and the corresponding CBs and the VBs:
horizontally drawing the obtained CP analysis result diagram of the
material and the energy difference diagram between the CBs and the
VBs side by side, such that energy ranges and scales of
longitudinal coordinates of the two diagrams are completely
consistent and aligned;
using a series of horizontal lines to indicate the positions of CPs
in the CP analysis result diagram, making the horizontal lines to
traverse into the energy difference diagram, and determining the
CBs and the VBs participating in the formation of the CPs according
to tangent points of the horizontal lines and curves in the energy
difference diagram; and
determining the spatial positions of the CPs by indicating the
above-mentioned tangent points in the BZ.
Preferably, the particle type determination module adopts following
steps to indicate the CBs and the VBs in the energy band structure
diagram:
drawing the energy band structure diagram of the step S2 right
above the energy difference diagram to make it consistent with the
high symmetry points of the BZ covered by horizontal coordinates of
the energy difference diagram, where scales of the high symmetry
points in the two diagrams are aligned with each other; and
drawing a straight line perpendicular to the upper energy band
structure diagram from the tangent points on the curves of the
energy difference diagram, wherein two points where the straight
line intersects with the energy band structure diagram indicate the
CBs and the VBs participating in formation of the CPs, so as to
indicate the CBs and the VBs in the energy band structure
diagram.
Preferably, the particle type determination module adopts following
steps to determine the type of the particles participating in
formation of the CPs:
drawing the PDOS diagram at one side of the energy band structure
diagram, so that the energy ranges of the longitudinal coordinates
thereof and the longitudinal coordinates of the band structure
diagram are consistent, and the scales of the two longitudinal
coordinates are aligned; and
drawing straight lines horizontally from the CBs and the VBs
indicated in the energy band structure diagram and extending the
same to the PDOS diagram, and directly reading out the type of the
particles participating in the formation of the CPs in the PDOS
diagram by analyzing intersections of the straight lines with
spectral lines in the PDOS diagram.
In overall, compared with the prior art, the above technical scheme
conceived by the invention has following technical advantages:
1. The invention utilizes a CP analysis to perform fitting analysis
on the second derivative spectrum of the material dielectric
function to obtain specific information of the material CPs, and
combined with the energy band structure diagram, the PDOS diagram
and the energy difference diagram to accurately identify the energy
levels and particle type associated with the formation of the
material CPs, the system of the invention has comprehensive and
specific theoretical support, and is suitable for in-depth analysis
of optical transition characteristics of various materials, and has
broad application prospects.
2. By synthetically utilizing information of the CP analysis
result, the energy band structure diagram, the PDOS diagram and the
energy difference diagram, the optical transition mechanism of the
material is revealed, and the spatial position, the particle type
and the involved energy band of the material optical transition can
be determined systematically and comprehensively, which realizes
organic combination of theory and experiment results, and
effectively solves the problem of inaccurate and incomplete
analysis results of the existing analytical method.
3. The invention also provides the concrete operation steps and
means of how to determine the spatial positions of the CPs, the
corresponding CB and VB, and the type of the particles involving in
the formation of the CPs by using the CP analysis result diagram,
the energy band structure diagram, the PDOS diagram and the energy
difference diagram, which has guiding significance for practical
operations and applications.
BRIEF DESCRIPTION OF THE DRAWINGS
The accompanying drawings are included to provide a further
understanding of the invention, and are incorporated in and
constitute a part of this specification. The drawings illustrate
embodiments of the invention and, together with the description,
serve to explain the principles of the invention.
FIG. 1 is a flowchart illustrating a material optical transition
analysis method according to an embodiment of the invention.
FIG. 2 is a schematic diagram of ellipsometric measurement of a
single-layer WSe.sub.2 on a sapphire substrate according to an
embodiment of the invention.
FIG. 3 is a measurement and fitting ellipsometric spectrum of the
single-layer WSe.sub.2 in an energy range of 0.73-6.42 eV according
to an embodiment of the invention.
FIG. 4 is a dielectric function spectrum of the single-layer
WSe.sub.2 over the energy range of 0.73-6.42 eV according to an
embodiment of the invention.
FIG. 5 is a CP analysis result of the single-layer WSe.sub.2
according to an embodiment of the invention, in which (a) is an
analysis result of a low-energy band CP, (b) is an analysis result
of a high-energy band CP.
FIG. 6 is an energy band structure diagram and a PDOS diagram of
the single-layer WSe.sub.2 obtained from the first-principles
calculations according to an embodiment of the present invention,
in which (a) is the energy band structure diagram of the
single-layer WSe.sub.2, and (b) is the PDOS diagram of the
single-layer WSe.sub.2.
FIG. 7 is a spatial distribution diagram of energy differences of
CBs and VBs of the single-layer WSe.sub.2 according to an
embodiment of the invention.
FIG. 8 is a diagram showing spatial positions of CPs, related
energy band, and a related particle type in a single-layer
WSe.sub.2 dielectric function spectrum according to an embodiment
of the invention, in which (a) is an energy band structure diagram
of the single-layer WSe.sub.2, (b) is a PDOS diagram of the
single-layer WSe.sub.2, (c) is an energy difference spatial
distribution diagram of the CBs and VBs of the single-layer
WSe.sub.2, (d) is a CP analysis result of the single-layer
WSe.sub.2 dielectric function spectrum.
DESCRIPTION OF THE EMBODIMENTS
Reference will now be made in detail to the present preferred
embodiments of the invention, examples of which are illustrated in
the accompanying drawings. It should be understood that the
specific embodiments described herein are merely used for
explaining the invention and are not intended to be limiting of the
invention. Furthermore, the technical features involved in the
various embodiments of the invention described below may be
combined with each other as long as they do not conflict with each
other.
A basic principle of the invention is as follows. A CP analysis is
performed on a second derivative spectrum of a dielectric function
of a material to obtain center energy information thereof; and then
an energy band structure and a PDOS of the material are obtained
through, for example, a first-principles calculation, and a
difference processing is performed to a CB and a VB in the energy
band structure diagram of the material to draw an energy difference
curve of the CB and the VB; finally, a CP analysis result, the
energy difference curve of the CB and the VB, an energy band
structure diagram, a PDOS diagram are sequentially drawn, so as to
accurately identify an energy level and particle types related to
the formation of the CP in the dielectric function spectrum of the
material with assistance of an energy band nesting theory, and
determine a formation position of the CP in the BZ. The method
realizes analysis and interpretation of the optical transition
characteristics of a materials from the perspective of physics,
which has a more solid theoretical basis, a clear operation
process, and accurate and reliable analysis results, and it is
suitable for in-depth analysis and understanding of optical
transitions of various materials.
As shown in FIG. 1, an embodiment of the invention provides a
material optical transition analysis method, which is adapted to
analyze and interpret the optical transition characteristics of the
material at the physical level, and for any material, the method
includes the following steps:
S1: obtaining a dielectric function spectrum .epsilon.(E) of a
material to be analyzed over a specified band according to an
actual requirement, which may be obtained by means of experimental
measurements and literature (database) consulting, etc.;
calculating a second derivative spectrum of the dielectric function
spectrum .epsilon.(E) with respect to excitation light energy E:
d.sup.2.epsilon.(E)/dE.sup.2; the CPs of the material are the
positions where the optical transitions occur, so that a CP fitting
analysis is performed on the obtained second derivative spectrum of
the dielectric function to obtain detailed parameter information of
CPs in the dielectric function spectrum and a CP analysis result
diagram, where a detailed fitting equation is:
.times..function..times..function..times..function..times..times..PHI..ti-
mes..times..GAMMA..times..noteq..function..times..times..PHI..times..times-
..GAMMA..times. ##EQU00001##
Where, Amp, .PHI., E.sub.0 and .GAMMA. are respectively the
amplitude, the phase, the center energy and the damping coefficient
of the CP, i is the imaginary unit, m represents the wave vector
(K=(k.sub.x, k.sub.y, k.sub.z)) dimension of the optical transition
involved at the CP, and when m=1/2, 0, -1/2, it represents that the
wave vector dimension is respectively 1, 2 and 3; and when m=-1, it
represents that the exciton behaviour is presented at the CP; a
specific selection of the m value can be obtained by consulting a
literature.
S2: calculating a material energy band structure and a PDOS
(Partial Density of States):
obtaining the material energy band structure and the PDOS through
the first-principles calculations, and then drawing an energy band
structure diagram and a PDOS diagram of the material; and drawing
an energy difference diagram (i.e. a .DELTA.E(k) diagram) between
the CBs and the VBs in the energy band structure diagram of the
material. To be specific, the energy difference is calculated
through an equation
.DELTA.E.sub.ij(k)=E.sub.CB.sup.i(k)-E.sub.VB.sup.j(k) according to
the obtained energy band structure diagram, and then the energy
difference diagram between the CBs and the VBs is drawn, where
E.sub.CB.sup.j(k) represents the i.sup.th CB, E.sub.VB.sup.j(k)
represents the j.sup.th VB;
S3: determining the CB and the VB participating in formation of the
CP and a spatial position of the CP: horizontally drawing the CP
analysis result diagram obtained in the step S1 and the .DELTA.E(k)
diagram obtained in the step S2 side by side, such that energy
ranges and scales of longitudinal coordinates of the two diagrams
are completely consistent and aligned;
using a series of horizontal dotted lines to indicate positions of
the CPs in the CP analysis result diagram, and making the
horizontal dotted lines to horizontally traverse into the
.DELTA.E(k) diagram;
determining the CBs and the VBs participating in the formation of
the CPs by analyzing the tangent situation between the horizontal
dotted lines and the curves in the .DELTA.E(k) diagram;
determining the spatial positions of the CPs by indicating the
above-mentioned tangent points in the BZ.
The above two points are mainly based on an energy band nesting
theory, and a detailed equation thereof is:
.times..DELTA..times..times..pi..times..intg..times..gradient..times..gra-
dient..times..times..pi..times..intg..times..gradient..times..DELTA..times-
..times. ##EQU00002##
Where, JDOS is joint density of states, which almost determines a
transition strength of carriers in the material, S.sub.k is the
constant surface energy, which can be defined by .DELTA.E. When
|V.sub.k.DELTA.E(k)|=0, the JDOS can have a singular value, and it
is most likely to form a carrier transition. The following two
situations can lead to the singular JDOS, one situation is
.gradient..sub.kE.sub.CB.apprxeq..gradient..sub.kE.sub.VB.apprxeq.0,
and such situation generally occurs at high symmetry points of the
BZ, at these positions, changing rates of the CB and VB curves of
the material in a certain spatial direction are zero at the same
time to finally form the singular JDOS; another situation is
.gradient..sub.kE.sub.CB.apprxeq..gradient..sub.kE.sub.VB.noteq.0,
and now the changing rates of the CB and VB curves of the material
in a certain spatial direction are almost the same and none zero,
which results in
.gradient..sub.kE.sub.CB-.gradient..sub.kE.sub.VB.apprxeq.0, so as
to make the JDOS singular. The second unique energy band phenomenon
is particularly prominent in low-dimensional materials, which is
generally referred to as energy band nesting, where the CB and the
VB in the energy band structure are almost parallel to each other.
Both of the above two situations are covered by the point where the
spatial variation rate of the energy difference curve .DELTA.E(k)
of the CB and the VB is zero. Therefore, tangents of the curves in
.DELTA.E(k) and the horizontal dotted lines indicating the center
energy of the CPs are most likely to be positions at which these
CPs are formed, and then by observing and analyzing which CB and VB
are used to obtain the curve tangent to the horizontal dotted lines
through the difference calculation, the CB and VB related to the
formation of the CPs can be determined.
S4: indicating the CBs and the VBs in the material energy band
structure diagram participating in formation of each of the CPs,
and determining a type of particles participating in formation of
the CPs in the material PDOS diagram:
indicating energy bands participating in the formation of the CPs
in the energy band structure diagram based on the CBs and VBs
identified in the step S3, to be specific, drawing the energy band
structure diagram obtained in the step S2 right above the
.DELTA.E(k) diagram to make it consistent with the high symmetry
points of the BZ covered by horizontal coordinates of the
.DELTA.E(k) diagram, where scales of the high symmetry points in
the two diagrams are aligned with each other horizontally; and
drawing a series of vertical dotted line from the tangent point
determined in the step S3 to intersect with corresponding energy
levels in the above energy band structure diagram, so as to
indicate the CBs and the VBs participating in the formation of each
of the CPs in the energy band structure diagram.
The step of determining the type of the particles participating in
the formation of the CPs in the material PDOS diagram includes: in
case that the energy levels participating in the formation of the
CPs have been determined, the PDOS diagram can be introduced to
further determine the type of the particles participating in the
formation of the CPs (orbits where electrons are located, atoms
that provide the electrons, etc.) and qualitatively analyze a
participation proportion of each particle. To be specific, drawing
the PDOS diagram to the right of the energy band structure diagram
to ensure consistence of longitudinal coordinates thereof with
longitudinal coordinates of the energy band structure diagram, and
alignment of scales of the two diagrams; drawing a series of
horizontal dotted lines from the energy levels of each of the CPs
to extend into the PDOS diagram, so as to read out the type of the
particles participating in formation of each CP from the PDOS
diagram and analyze a participation degree thereof.
An embodiment is provided below, and in the embodiment, a
spectroscopic ellipsometer is adopted to measure an ellipsometric
spectrum of a single-layer WSe.sub.2 on a sapphire substrate
(referring to FIG. 2), and a dielectric function spectrum of
WSe.sub.2 is obtained through analysis. Then, physical causes of
optical transitions in the single-layer WSe.sub.2 are deeply
discussed by using CP analysis, first-principles calculations and
energy band nesting theory, and detailed implementation steps are
as follows:
(1) determining the dielectric function spectrum of a specified
band of the single-layer WSe.sub.2:
the spectroscopic ellipsometer is adopted to measure an
ellipsometric parameter spectrum [.PSI., .DELTA.] of the
single-layer WSe.sub.2, where tan .PSI. and .DELTA. represent an
amplitude ratio and a phase difference of p-polarized light and
s-polarized light, the energy range of the ellipsometric
measurement is 0.73-6.42 eV, the incident angle
.theta..sub.i=65.degree., and the obtained ellipsometric spectrum
of the single-layer WSe.sub.2 is drawn in FIG. 3. By fitting the
ellipsometric spectrum of the single-layer WSe.sub.2 with a
combined oscillator dielectric function model
(6Lorentz+2Cody-Lorentz), the dielectric function spectrum shown in
FIG. 4 is obtained, where the dielectric function spectrum shows
seven discernible CPs (A-G) (including the maximum points and the
shoulder points).
(2) Solving a second derivative spectrum of the single-layer
WSe.sub.2 dielectric function spectrum
data processing software OriginPro 9.1 is used to calculate the
numerical second derivative of the single-layer WSe.sub.2
dielectric function spectrum with respect to the excitation light
energy.
(3) CP analysis (i.e. using the equation (1) to fit the second
derivative spectrum of the dielectric function of the material to
obtain the detailed information of each CP in the dielectric
function spectrum, which includes the center energy E.sub.0, the
damping coefficient .GAMMA., the amplitude Amp, and the phase
.PHI..)
CP analysis is performed to the second derivative spectrum of the
single-layer WSe.sub.2 dielectric function spectrum. By referring
to the existing literatures, the parameter m of the equation (1)
can be set to -1, which can describe the exciton transitions
occurred at the CPs. Considering that an amplitude of the second
derivative spectrum in a low-energy band is much larger than that
in a high-energy band, the spectral characteristics of the
high-energy band are easily neglected if the whole spectrum is
subjected to a uniform CP fitting analysis. Therefore, the CP
analysis is performed to the second derivative spectrum in two
energy bands, which are respectively a low-energy band (1.50-2.20
eV) and a high-energy band (2.20-6.42 eV), and there is no obvious
CP in the dielectric function spectrum of the energy band lower
than 1.50 eV, which is not analyzed. Finally, the center energies
of 7 CPs are respectively 1.67 eV, 2.09 eV, 2.42 eV, 2.89 eV, 3.39
eV, 4.01 eV, 4.66 eV, and CP fitting analysis result is plotted in
FIG. 5.
(4) Calculating and drawing an energy band structure diagram and a
PDOS diagram of the single-layer WSe.sub.2
the energy band structure and the PDOS of the single-layer
WSe.sub.2 are calculated by the first-principles software package
Vienna ab initio package (VASP v5.4.1) based on the density
functional theory (DFT), the most stable 2H crystal configuration
of the WSe.sub.2 is adopted in this calculations, and the
single-layer WSe.sub.2 has 15 .ANG. vacuum layers on top and bottom
to minimize the influence of interlayer interaction on final
calculation results as far as possible. The Perdew-Burke-Ernzerhof
(PBE) functional based on the plane wave (PAW) pseudopotential is
adopted to optimize the crystal configuration, and the force and
total energy convergence criteria during the optimization process
are 0.01 eV/A and 10.sup.-5 eV, respectively. The calculation of
the energy band structure and the PDOS is accomplished by using the
PAW-based hybrid functional Heyd-Scuseria-Ernzerhof (HSE06), where
a kinetic energy cut-off energy in the calculation is set to 700
eV, the BZ grid is divided into 8.times.8.times.1, and the
integration path is: .GAMMA.-K-M-.GAMMA.. In order to accurately
simulate the energy band splitting phenomenon caused by the strong
spin-orbit coupling (SOC) in the single-layer WSe.sub.2, the SOC
effect is taken into account in the calculations, the calculated
energy band structure and the PDOS of the single-layer WSe.sub.2
are drawn in FIG. 6.
(5) drawing an energy difference diagram between the CBs and VBs of
the single-layer WSe.sub.2
Considering a center energy range of the CPs of the single-layer
WSe.sub.2, only the differences between the first four levels of
CBs and the first four levels of VBs in the energy band structure
are calculated to obtain 16 energy difference curves
.DELTA.E.sub.ij(k)(i=1, 2, 3, 4; j=1, 2, 3, 4) as shown in FIG. 7.
A reason of selecting the first four levels of the CBs and the VBs
is that when the first four levels of the CBs and the VBs are
selected, all the corresponding .DELTA.E.sub.ij(k) values in the BZ
have exceeded the center energy value of the CP G, and it is
meaningless to use the higher CBs and VBs for the difference
processing. Therefore, when the values of .DELTA.E.sub.ij(k) in the
BZ have all been greater than the center energy of the CP with the
highest energy, the difference processing can be stopped.
(6) Determining the CBs and VBs related to the formation of the CPs
in the WSe.sub.2 dielectric function spectrum and forming positions
of the CPs in the BZ:
two result diagrams obtained through high-energy and low-energy CP
analysis in FIG. 5 are spliced into one (FIG. 8(d)), and the energy
is taken as the longitudinal axis, the .DELTA.E.sub.ij(k) diagram
obtained in the step (5) is drawn to the left of the CP analysis
result to ensure consistence of energy intervals of longitudinal
coordinates of the two diagrams (which are all 1.5-6.0 eV) and
vertical alignment of scales; a series of horizontal dotted lines
are used to indicate center energy positions of the above 7 CPs in
the CP analysis diagram and are connected to the .DELTA.E.sub.ij(k)
diagram, and tangent points of the horizontal dotted lines and
curves in the .DELTA.E.sub.ij(k) diagram indicate the positions of
the CPs. By analyzing which CBs and VBs are used to obtain the
curves tangent to the horizontal dotted lines through the
difference calculation, the energy levels participating in the
formation of the CPs may be deduced reversely. To be specific, as
shown in FIG. 8(c,d), both of CP A and CP B in the single-layer
WSe.sub.2 dielectric function spectrum are formed at the high
symmetry point K in the BZ, and the CBs participating in formation
of the CP A and the CP B are CB.sub.1-2, and the VB associated with
the CP A is VB.sub.1, and the VB associated with the CP B is
VB.sub.2. Since the curve tangent to the dotted line passing
through the center energy of the CP C does not appear in FIG. 8(c),
the energy levels participating in the formation of the CP C cannot
be specifically determined, and energy band projection calculation
is required for further judgment. CPs D and E are all formed
between F and K points of the BZ, which are related to energy band
nesting, the formation of the CP D is related to transition of
electrons from VB.sub.1 to CB.sub.1, and the formation of CP E is
related to transition of electrons from VB.sub.2 to CB.sub.2. CP F
is formed at a high symmetry point M of the BZ, and multiple
transitions of electrons from VB.sub.1-2 to CB.sub.1-2 are its main
cause. The high-energy CP G is formed at the high symmetry point K
of the BZ, which is related to the multiple transitions of
electrons from VB.sub.3-4 to CB.sub.1-2.
(7) indicating the CBs and VBs participating in the formation of
the CPs in the energy band structure diagram of the single-layer
WSe.sub.2
in order to intuitively display the CBs and VBs related to the CP
formation, the energy band structure diagram calculated in the step
(4) is drawn right above the .DELTA.E.sub.ij(k) figure, and the
high symmetric points of horizontal coordinates of the two diagrams
are horizontally aligned; some vertical dotted lines are drawn from
the tangent points determined in the step (6) (gray dots in FIG.
8(c)) to extend to the energy band structure diagram (FIG. 8(a)).
According to the analysis result of the step (7), some upward
arrows (arrow direction represents the main transition direction)
are used to sequentially indicate the CBs and VBs participating in
the formation of the CPs in FIG. 8(a).
(8) Determine the type of particles participating in the formation
of each CP in the PDOS diagram of the single-layer WSe.sub.2
in order to identify the particle types (orbits where electrons are
located and atoms that provide the electrons) participating in the
CP formation, the PDOS diagram calculated in the step (4) is drawn
to the right of the energy band structure diagram, and the energy
intervals of the longitudinal coordinates are ensured to be
consistent (which are all -4.5-5 eV), and the scales are vertically
aligned; some horizontal dotted lines are drawn from heads and
tails of the arrows indicated in the step (7) to connect the energy
band structure diagram and the PDOS diagram, so as to identify the
particles related to the CP formation. To be specific, as shown in
FIG. 8(b), the particles participating in the formation of the CPs
in the single-layer WSe.sub.2 dielectric function spectrum are
mainly electrons of an Se 4p orbit and a W 5d orbit, where the
electrons of the Se 4p orbit dominate the CPs A-F, and the
electrons of the W 5d orbit only influence the VBs of the CP G.
In summary, the material optical transition analysis method of the
invention utilizes a CP analysis theory to perform fitting analysis
on the second derivative spectrum of the material dielectric
function to obtain the CP analysis result diagram and specific
parameter information of the material CPs, and combined with the
energy band structure diagram, the PDOS diagram and the energy band
nesting theory (i.e. the CBs and the VBs are determined by the
tangents of the horizontal dotted lines passing through the CPs and
the E(k) curves), so as to accurately identify the energy levels
and particle types associated with the formation of the CPs, and by
skillfully combining the CP analysis result of the dielectric
function spectrum and the energy band structure/PDOS, in-deep
analysis in a physical aspect of the optical transitions exhibited
in the material dielectric function spectrum is performed. Compared
with the existing optical transition analysis methods, the CP
positions determined according to the method of the invention are
more accurate, and the energy levels and particle types associated
with the CP formation can be accurately located, the method is more
comprehensive and has more solid theoretical support, which is
suitable for in-depth analysis of the optical transition
characteristics of various materials and has broad application
prospects.
In the above specific analysis process, only the single-layer
WSe.sub.2 on the sapphire substrate is taken as an example for
description, and the optical transition analysis of the other types
of materials may also be operated according to the same method.
The method of the invention is not limited to the specific
embodiments mentioned above, and general technicians of the field
can implement the invention in a variety of other specific
embodiments according to the contents disclosed by the invention,
for example, to use other methods or instruments that can obtain
the material dielectric function spectrum, other analytical bands,
other software packages or codes that can calculate the material
energy band structure and the PDOS, etc. Therefore, any design that
adopts the principle and idea of the design method of the invention
and makes some simple changes or modifications falls into a
protection scope of the invention.
* * * * *